Question

Question 5 Multiple Choice Worth 4 points)

Which expression is equivalent to (5^3)-^2?

1/5^3

-1/5.5.5.5.5.5

5^3

1/5.5.5.5-5.5

Answer 1

`\large\boxed{(1)/(5\cdot5\cdot5\cdot5\cdot5\cdot5)}`

Explanation:

`\text{Use}\ (a^n)^m=a^(nm)\\\\(5^3)^(-2)=5^((3)(-2))=5^(-6)\\\\\text{use}\ a^(-n)=(1)/(a^n)\\\\=(1)/(5^6)\\\\\text{use}\ a^n=\underbrace{a\cdot a\cdot a\cdot ...\cdot a}_(n)\\\\=(1)/(5\cdot5\cdot5\cdot5\cdot5\cdot5)`